1. Field of the Invention
The invention concerns laser ranging including space laser ranging. It concerns in particular satellite laser ranging (SLR). SLR measures the time for a laser pulse to make the return trip between a laser ground station and a target carried by a satellite (or vice versa), for example, and then converts the measured time into an (instantaneous) distance between a reference point of the laser station and the center of mass of the satellite, including correction of various deterministic effects. SLR includes the situation in which the distance measured is that between two artificial satellites, between a satellite and a target on the ground, and even more generally between natural or artificial heavenly bodies.
2. Description of the Prior Art
It is as well to remember that all "laser" satellites in earth orbit at this time (such as the LAGEOS I and II, AJISAI, STARLETTE, and STELLA satellites) were designed at a time when SLR was a relatively imprecise art and the lasers employed were low-power devices (as compared to what is possible today). These satellites were therefore optimized for targets composed of many (from 60 to more than 2,000) small "cube corner" retroreflectors capable of sending back a detectable quantity of light to the transmitter station regardless of the orientation of the satellite. It was not very important if for any laser firing they were not all exactly the same distance from the transmitter station, to within a few centimeters or even decimeters.
The situation has changed greatly in the past few years with the result that current SLR stations can use pulse durations as low as about ten picoseconds (1 ps=10.sup.-12 seconds), and the measurement accuracy on a single echo is approaching one millimeter. This does not apply to the final measurement accuracy because of the multiplicity of echos (one echo from each retroreflector visible to the transmitter at the time of firing), which causes temporal spreading of the return pulses (in respect of which the term "signature" is sometimes used), which echoes cannot be individually and precisely associated with the instantaneous distance to the center of mass of the satellite.
Even with highly sophisticated SLR tools, this effect makes it virtually impossible to determine the distance of laser satellites with an absolute accuracy better than one centimeter from a single pulse, and even this is possible only in specific cases with small satellites.
For completeness, it should be mentioned that the relative transverse speed between the satellite and the laser station causes a speed aberration phenomenon that is corrected on existing satellites by imposing small differences ("errors") on the angles between the reflective faces of the cube corners relative to the nominal value of 90.degree..
The cube corners are usually solid and are deliberately made small (length of diameter 3 cm to 4 cm) for two reasons:
the diffraction pattern of the lightwave that they reflect constitutes a sort of continuous ring whose radius and width correspond to the values needed for adequate compensation of the speed aberration, rather than six distinct and separate lobes (this is the effect of the small angle errors); and
because of the small size of the cube corners, the temperature gradients likely to arise within the glass from which the cube corners are made remain small and consequently have little effect in terms of degradation of the resultant diffraction pattern.
Given this background, the need arises to satisfy the following requirements to the greatest possible degree:
.alpha.--to return a sufficient quantity of flux (energy) to the receiver of the transmitter station by adequate correction of the speed aberration, combined with minimizing of the temporal "signature" (it is accepted that it is not essential for the retroreflective efficacy of the satellite to be constant during (largely unknown) movements of the satellite);
.beta.--to eliminate any influence likely to broaden the pulses sent back by the satellite;
to obtain a virtually null uncertainty (ideally 1 mm or less) in the determination of the distance between a reference point of the laser station and the center of mass of the satellite from measurements of the retroreflector distance, regardless of the angles of incidence of the light pulses on the satellite; and
.delta.--to maximize the density of the system to minimize disturbances from non-gravitational forces.
In the context of the Earth remote sensing requirements mentioned above, European Patents A 0,506,517, A 0,571,256 and French Patent 2,691,129 describe the assembly of a small number of large retroreflectors on a common structure to constitute a remote sensing microsatellite enabling existing and future stations to achieve millimeter measurement accuracy in measurement of large distances.
The use of large cube corner retroreflectors (CCR) which are hollow rather than solid as on present day satellites should make it possible to achieve an appropriate energy balance for the satellite plus CCR system. Given the energy and the duration of the pulses transmitted by modern SLR stations, assuming orbit altitudes between 300 km and 6,000 km for this type of satellite, and given the angular spreading of the energy retroreflected by the CCR and the typical size of the receiving telescope in a station of this kind (pupil diameter in the order of 50 cm), it can be shown that a single retroreflector having a diameter typically between 10 cm and 20 cm should be able to satisfy the energy balance requirements of the system.
In a preferred embodiment described in French Patent A 2,691,129, the target is formed by eight cube corners having their apexes close together.
In this instance only rays at grazing incidence to the reflective face of one cube corner (and consequently of null efficacy with respect to return to the transmitter station) can be in the field of view of one or more adjacent CCR. As this is a rare case, it can be assumed that this configuration is characterized by non-overlapping fields of view of the retroreflectors, i.e. a single echo detected on return.
The question then arises of determining the distance to the center of mass (or any other reference point) of the target from a single echo sent back by a CCR whose apex is at a distance from the center of mass (or reference point) when it is necessary to dispense with any demands in terms of attitude control or, more generally, any demands in respect of the relative orientation of the laser transmitter/receiver (E/R) and the CCR (the latter can be on the Earth or on the Moon and the T/R trajectory has a random orientation relative to that of the CCR).
In other words, the problem is to deduce, from the distance between the E/R reference point and the apex of the CCR that can be measured by means of a single echo sent back by the CCR, the distance between a reference point of the E/R and a reference point associated with the CCR at a distance from the apex of the CCR when:
the position of the reference point associated with the CCR relative to the apex of the latter is known;
but the orientation relative to the CCR of the direction in which the CCR receives and returns the laser radiation forming the echo is not known a priori.
When the CCR is on a satellite (which is a small body in practice), the associated reference point is usually the center of mass of the satellite. In this case, the center of mass preferably has the same position relative to each CCR if the satellite carries a plurality of CCR adapted to return a single echo. More generally, if the CCR is part of a plurality of CCR mounted on a common support structure fixed relative to a natural or artificial object (Earth, Moon, or satellite of any size), the reference point is chosen to have the same position relative to each CCR. In the simplest case, this CCR reference point is on the normal of each CCR at the same distance d.sub.o from the apex S of the CCR (at least approximate convergence of the normals to all the CCR at one and the same point is then an installation constraint in respect of the CCR). The simple case generalizes to a single CCR whose reference point O is at a negative distance d.sub.o from the apex S on the normal n of the CCR. This distance d.sub.o is sometimes called the "optical constant".
This optical constant is the correction to be applied to the measured distance (E/R - CCR apex) to obtain the distance to the reference point along the normal to the CCR. As shown in FIG. 1, for a ray at any angle of incidence i to the normal, the corresponding value of the correction d is less than d.sub.o and depends on i. The value of d is given by the expression d=d.sub.o cos(i). The mean value (d.sub.avg) of d and the excursions --called errors .delta.--relative to this mean depend on d.sub.o and on all of the angles of incidence i for which the measurements can be made. For example, if the measurements can be made only for rays within a cone having a half-angle of 35.degree. to the normal of the CCR (i.e. for i.ltoreq.35.degree.), it can be shown that d.sub.avg has a value of approximately 0.9d.sub.o and that the maximum errors .delta. relative to d.sub.avg reach a value of .+-.0.1d.sub.0. Taking d.sub.o =5 cm, an average value d.sub.avg close to 4.5 cm is obtained, with maximum errors such that -0.5 cm.ltoreq..delta..ltoreq.+0.5 cm.
As described in European Patent A 0,571,256, the correction required to the distance to the apex S to obtain the distance to the reference point O (if i varies between 0.degree. and 35.degree. in any direction transverse to the normal of the CCR) varies between 0.8d.sub.o and d.sub.o. In other words, 0.9d.sub.o is an estimate of this correction to the nearest 0.1d.sub.o.